Jones told The Star on Wednesday her application had been approved by district court judge K D Kelly.
"I'm really pleased that the judge has accepted arguments for a recount, despite council's opposition for a recount," she said.
Jones lost the seat to Innes Ward councillor and new Deputy Mayor Pauline Cotter by 16 votes in the October election.
She filed her recount the following Tuesday on October 18.
Jones' application mentioned the closeness of the election and raised concerns about the collation and counting of the special votes, specifically at the Beckenham Service Centre.
Staff had been told they did not need to sign the forms for the votes or witness the voting, contrary to instructions on the form for casting a special vote.
Electoral officer Jo Daly acknowledged she did instruct them in that way and admitted her instructions were inconsistent but only at that centre.
Judge Kelly was satisfied that Jones' concerns about the inconsistencies in special voting constituted a reasonable belief that the election result could be incorrect and Jones could be elected if the votes were recounted.
Overall, 37 votes were declared informal because the accompanying special voting declarations were not witnessed.
The judge instructed the recount should be conducted using the same specialised electronic scanning equipment used in the original count, but all informal, blank and special equipment should be individually reviewed by the overseeing judge.
Jones said she was also "very grateful to my ... lawyers at Taylor Shaw".
Her application had raised some issues with the special votes and how they were collated and received.
Said a Christchurch City Council spokesperson: "As directed in the decision a recount will take place in Christchurch and preferably occur no later than 8 November. The date is not yet established."
Jones said she is keen to see the recount take place as soon as possible.
"Clearly there's a need to get on with it now and get it sorted once and for all," Jones said.
"Let the recount begin," Jones said.
Meanwhile, Cotter says she will keep doing her job until she hears otherwise.
Said Cotter: "This is a process that Ali's choosing to undertake and we're just going to wait and see what the outcome is."
The acceptance of Jones' application comes as unsuccessful Waipuna Halswell-Hornby-Riccarton Community Board candidate, Luke Chandler, also had his application for a recount denied.
